The Principal Investigator plans to study several problems in design of experiments. The projection properties of orthogonal arrays and some other designs will be investigated. Recent research has shown that interesting projection properties of certain orthogonal arrays have important statistical implications. The newly introduced concept of estimation capacity, a measure of the capability of a design to handle and estimate different potential models involving interactions, will also be investigated. In addition to factorial designs, the Principal Investigator will study optimal and efficient regression designs under random block-effects models. Other proposed research includes the Principal Investigator's collaboration with Professor Ker-Chau Li on the study of dimension reduction techniques for the analysis of data from designed experiments. Such techniques, in conjunction with dynamic graphics, can help extract additional useful information that may not be provided by traditional analyses. The resulting design issues will also be studied. Experimental design is used extensively in a wide range of scientific and industrial investigations. In industrial experiments, often a large number of factors have to be studied, but the experiments are expensive to conduct. Fractional factorial designs are particularly useful to handle this problem. In recent years, factorial designs have received considerable attention, mainly due to the Japanese success in applying them to improve quality in industrial manufacturing. This re-surgence of interest provides an opportunity to re-examine some conventional wisdom. This will be given the highest priority in the Principal Investigator's research activities during the coming years. In addition to theoretical studies, good designs will also be constructed for experimenters' use. Other proposed research includes a problem arising from a recent optometry experiment, and the study of the performance of a new data-analyt ic tool on experimental data.
